已知1/x-1/2y=1/3,则代数式(2x+3xy-4y)/(x-3xy-2y)的值为
问题描述:
已知1/x-1/2y=1/3,则代数式(2x+3xy-4y)/(x-3xy-2y)的值为
答
(2x+3xy-4y)/(x-3xy-2y)
=(2/y+3-4/x)/(1/y-3-2/x) (分子分母除以xy)
=(-4/x+2/y+3)/(-2/x+1/y-3)
=[-4(1/x-1/2y)+3]/[-2(1/x-1/2y)-3 ]
=(-4*1/3+3)/(-2*1/3-3)
=(-4/3+3)/(-2/3-3)
=5/3 /(-11/3)
=-5/11